Newton, Isaac, Philosophia naturalis principia mathematica, 1713

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        <body>
          <chap>
            <p type="main">
              <s>
                <pb xlink:href="039/01/042.jpg" pagenum="14"/>
                <arrow.to.target n="note6"/>
              </s>
            </p>
            <p type="margin">
              <s>
                <margin.target id="note6"/>
              TA,
                <lb/>
              E</s>
            </p>
            <p type="main">
              <s>
                <emph type="center"/>
              COROLLARIUM II.
                <emph.end type="center"/>
              </s>
            </p>
            <p type="main">
              <s>
                <emph type="italics"/>
              Et hinc patet compoſitio vis directæ
                <emph.end type="italics"/>
              AD
                <emph type="italics"/>
              ex viribus quibuſvis
                <lb/>
              obliquis
                <emph.end type="italics"/>
              AB
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
              BD,
                <emph type="italics"/>
              & viciſſim reſolutio vis cujuſvis directæ
                <emph.end type="italics"/>
                <lb/>
              AD
                <emph type="italics"/>
              in obliquas quaſcunque
                <emph.end type="italics"/>
              AB
                <emph type="italics"/>
              &
                <emph.end type="italics"/>
              BD.</s>
              <s>
                <emph type="italics"/>
              Quæ quidem compoſitio
                <lb/>
              & reſolutio abunde confirmatur ex Mechanica.
                <emph.end type="italics"/>
              </s>
            </p>
            <p type="main">
              <s>Ut ſi de rotæ alicujus centro
                <emph type="italics"/>
              O
                <emph.end type="italics"/>
              exeuntes radii inæquales
                <emph type="italics"/>
              OM,
                <lb/>
              ON
                <emph.end type="italics"/>
              filis
                <emph type="italics"/>
              MA, NP
                <emph.end type="italics"/>
              ſuſtineant pondera
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              P,
                <emph.end type="italics"/>
              & quærantur vi­
                <lb/>
              res ponderum ad movendam rotam: Per centrum
                <emph type="italics"/>
              O
                <emph.end type="italics"/>
              agatur recta
                <lb/>
                <emph type="italics"/>
              KOL
                <emph.end type="italics"/>
              filis perpendiculariter occurrens in
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              L,
                <emph.end type="italics"/>
              centroque
                <emph type="italics"/>
              O
                <emph.end type="italics"/>
              &
                <lb/>
              intervallorum
                <emph type="italics"/>
              OK, OL
                <emph.end type="italics"/>
              majore
                <emph type="italics"/>
              OL
                <emph.end type="italics"/>
                <lb/>
                <figure id="id.039.01.042.1.jpg" xlink:href="039/01/042/1.jpg" number="2"/>
                <lb/>
              deſcribatur circulus occurrens filo
                <lb/>
                <emph type="italics"/>
              MA
                <emph.end type="italics"/>
              in
                <emph type="italics"/>
              D:
                <emph.end type="italics"/>
              & actæ rectæ
                <emph type="italics"/>
              OD
                <emph.end type="italics"/>
              pa­
                <lb/>
              rallela ſit
                <emph type="italics"/>
              AC,
                <emph.end type="italics"/>
              & perpendicularis
                <lb/>
                <emph type="italics"/>
              DC.
                <emph.end type="italics"/>
              Quoniam nihil refert, utrum
                <lb/>
              filorum puncta
                <emph type="italics"/>
              K, L, D
                <emph.end type="italics"/>
              affixa ſint
                <lb/>
              an non affixa ad planum rotæ; pon­
                <lb/>
              dera idem valebunt, ac ſi ſuſpende­
                <lb/>
              rentur a punctis
                <emph type="italics"/>
              K
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              L
                <emph.end type="italics"/>
              vel
                <emph type="italics"/>
              D
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              L.
                <emph.end type="italics"/>
                <lb/>
              Ponderis autem
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              exponatur vis to­
                <lb/>
              ta per lineam
                <emph type="italics"/>
              AD,
                <emph.end type="italics"/>
              & hæc reſolvetur
                <lb/>
              in vires
                <emph type="italics"/>
              AC, CD,
                <emph.end type="italics"/>
              quarum
                <emph type="italics"/>
              AC
                <emph.end type="italics"/>
              trahendo radium
                <emph type="italics"/>
              OD
                <emph.end type="italics"/>
              directe a cen­
                <lb/>
              tro nihil valet ad movendam rotam; vis autem altera
                <emph type="italics"/>
              DC,
                <emph.end type="italics"/>
              trahen­
                <lb/>
              do radium
                <emph type="italics"/>
              DO
                <emph.end type="italics"/>
              perpendiculariter, idem valet ac ſi perpendiculari­
                <lb/>
              ter traheret radium
                <emph type="italics"/>
              OL
                <emph.end type="italics"/>
              ipſi
                <emph type="italics"/>
              OD
                <emph.end type="italics"/>
              æqualem; hoc eſt, idem atque
                <lb/>
              pondus
                <emph type="italics"/>
              P,
                <emph.end type="italics"/>
              ſi modo pondus illud ſit ad pondus
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              ut vis
                <emph type="italics"/>
              DC
                <emph.end type="italics"/>
              ad
                <lb/>
              vim
                <emph type="italics"/>
              DA,
                <emph.end type="italics"/>
              id eſt (ob ſimilia triangula
                <emph type="italics"/>
              ADC, DOK,
                <emph.end type="italics"/>
              ) ut
                <emph type="italics"/>
              OK
                <emph.end type="italics"/>
                <lb/>
              ad
                <emph type="italics"/>
              OD
                <emph.end type="italics"/>
              ſeu
                <emph type="italics"/>
              OL.
                <emph.end type="italics"/>
              Pondera igitur
                <emph type="italics"/>
              A
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              P,
                <emph.end type="italics"/>
              quæ ſunt reciproce ut
                <lb/>
              radii in directum poſiti
                <emph type="italics"/>
              OK
                <emph.end type="italics"/>
              &
                <emph type="italics"/>
              OL,
                <emph.end type="italics"/>
              idem pollebunt, & ſic conſi­
                <lb/>
              ſtent in æquilibrio: quæ eſt proprietas notiſſima Libræ, Vectis, &
                <lb/>
              Axis in Peritrochio. </s>
              <s>Sin pondus alterutrum ſit majus quam in hac
                <lb/>
              ratione, erit vis ejus ad movendam rotam tanto major. </s>
            </p>
            <p type="main">
              <s>Quod ſi pondus
                <emph type="italics"/>
              p
                <emph.end type="italics"/>
              ponderi
                <emph type="italics"/>
              P
                <emph.end type="italics"/>
              æquale partim ſuſpendatur filo
                <emph type="italics"/>
              Np,
                <emph.end type="italics"/>
                <lb/>
              partim incumbat plano obliquo
                <emph type="italics"/>
              pG:
                <emph.end type="italics"/>
              agantur
                <emph type="italics"/>
              pH, NH,
                <emph.end type="italics"/>
              prior ho­
                <lb/>
              rizonti, poſterior plano
                <emph type="italics"/>
              pG
                <emph.end type="italics"/>
              perpendicularis; & ſi vis ponderis
                <emph type="italics"/>
              p
                <emph.end type="italics"/>
                <lb/>
              deorſum tendens, exponatur per lineam
                <emph type="italics"/>
              pH,
                <emph.end type="italics"/>
              reſolvi poteſt hæc in
                <lb/>
              vires
                <emph type="italics"/>
              pN, HN.
                <emph.end type="italics"/>
              Si filo
                <emph type="italics"/>
              pN
                <emph.end type="italics"/>
              perpendiculare eſſet planum aliquod
                <lb/>
                <emph type="italics"/>
              pQ,
                <emph.end type="italics"/>
              ſecans planum alterum
                <emph type="italics"/>
              pG
                <emph.end type="italics"/>
              in linea ad horizontem paral­
                <lb/>
              lela; & pondas
                <emph type="italics"/>
              p
                <emph.end type="italics"/>
              his planis
                <emph type="italics"/>
              pQ, pG
                <emph.end type="italics"/>
              ſolummodo incumberet; ur-</s>
            </p>
          </chap>
        </body>
      </text>
    </archimedes>
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